Polymer size

Brainard, P. Trefonas, J.H. Lammers, C.A. Cutler, J.F. Mackevich, A. Trefonas, and S.A. Robertson, Shot noise, LER and quantum efficiency of EUV photoresists, Proc. SPIE 5374, 74 85 (2004). 

Morisawa, N. Matsuzawa, Y. Kaimoto, M. Endo, T. Matsuo, K. Kuhara, andM. Sasago, Reduction of line edge roughness in the top surface imaging process, J. Vac. Set Technol. B 16(6), p. 3739 (1998) W. Hinsberg, E. Houle, G. Wallraff, M. Sanchez, M. Morison, J. Hoffnagle, H. Ito, 

Nguyen, C.E. Larson, P.J. Brock, and G. Breyta, Factors controlling pattern formation in chemi cally amplified resists at sub 100 nm dimensions, J. Photopolym. Set Technol. 12(4), 649 (1999) V. Rao, J. Hutchinson, S. Holl, J. Langston, C. Henderson, D.R. Wheeler, G. Cardinale, 

They observed that the aggregates trapped in the pattern sidewalls were similar to those in the unexposed regions of the film. 

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The increased acidity of the larger polymers most likely leads to this reduction in metal ion activity through easier development of active bonding sites in siUcate polymers. Thus, it could be expected that interaction constants between metal ions and polymer sdanol sites vary as a function of time and the sihcate polymer size. The interaction of cations with a siUcate anion leads to a reduction in pH. This produces larger siUcate anions, which in turn increases the complexation of metal ions. Therefore, the metal ion distribution in an amorphous metal sihcate particle is expected to be nonhomogeneous. It is not known whether this occurs, but it is clear that metal ions and siUcates react in a complex process that is comparable to metal ion hydrolysis. The products of the reactions of soluble siUcates with metal salts in concentrated solutions at ambient temperature are considered to be complex mixtures of metal ions and/or metal hydroxides, coagulated coUoidal size siUca species, and siUca gels. 

As in SEC, the surface chemistry of the HdC gels should be similar to that of the mobile phase and the solute. Otherwise, the retention time may increase as with the nonsize exclusion effects. However, the tolerance of PCHdC for a poorer mobile phase is better than SEC. The polymer size under 0 conditions has been studied using PCHdC (19). 

Another advantage of HdC is its generosity in terms of mobile-phase selection. The polymer size and solution properties of a polymer can be studied using HdC, especially OTHdC, in almost any solvent. In SEC, by comparison, the packing material and mobile phase have to be selected to prevent the nonsize exclusion effect. Because the instrumentation of HdC is similar to SEC, and the packing material and columns have become available commercially, this technique will gain in popularity. 

Gel permeation chromatograms actually give information about molecular size. For any polymer, size is determined hy a number of factors. These include not only molar mass but also temperature and thermodynamic quality of the solvent. Hence the relationship between size and molar mass is unique for each particular polymer-solvent combination, and we caimot assume that because two peaks of different polymers, even in the same solvent at the same temperature, have the same elution volume their molecules have the same molar mass. 

Trathnigg, B., Feichtenhofer, S., and Kollroser, M., Quantitation in liquid chromatography of polymers size-exclusion chromatography with dual detection, /. Chromatogr. A, 786, 75, 1997. 

Given that the primary step in the formation of NPSs is the infiltration of macromolecules into the porous silica matrix, the polymer size is an important parameter. Low molecular weight PEs are preferred for infiltration into the pores of the APTS-BMS spheres, and this process can be promoted by tuning the adsorption... 

Polysaccharide solubility in aqueous solutions usually is dependent on polymer size and its allied three-dimensional structure. Even water-insoluble carbohydrates may be solubilized by controlled hydrolysis of o-glycosidic linkages to create smaller polysaccharide molecules. Thus, cellulose may be solubilized by heating in an alkaline solution until the polymers are broken up sufficiently to reduce their average molecular weight. Many such soluble forms of common polysaccharides are available commercially. 

Flocculation rate limitation. The adsorption step was rate limiting for the overall flocculation process in this system. Polymer adsorption rate measurements for dispersed systems reported in the literature (2,26) do not lend themselves to direct comparisons with the present work due to lack of information on shear rates, flocculation rates, and particle and polymer sizes. Gregory (12) proposed that the adsorption and coagulation halftimes, tA and t, respectively, should be good indications of whether or not the adsorption step is expected to be rate limiting. The halftimes, tA and t, are defined as the times required to halve the initial concentrations of polymer and particles, respectively. Adsorption should not limit the flocculation rate if... 

The first section, Chemical Reactions on Polymers, deals with aspects of chemical reactions occurring on polymers—aspects relating to polymer size, shape, and composition are described in detail. One of the timely fields of applications comprises the use of modified polymers as catalysts (such as the immobilization of centers for homogeneous catalysis). This topic is considered in detail in Chapters 2, 3, 8, 9, and 11 and dealt with to a lesser extent in other chapters. The use of models and neighboring group effect(s) is described in detail. The modification of polymers for chemical and physical change is also described in detail in Chapters 2 (polystyrene) 4 (polyvinyl chloride) 5 (polyacrylic acid, polyvinyl alcohol, polyethyleneimine, and polyacrylamide) 6 (polyimides) 7 (polyvinyl alcohol) 8 (polystyrene sulfonate and polyvinylphosphonate) 10 (polyacrylamide) and 12 (organotin carboxylates). 

To improve the adhesion and interaction in the zeolite/polymer interface, the surface of the zeolites can also be sized (or primed ) by coating the zeolite with an ultrathin layer of the matrix polymer or a different polymer. Sizing of the zeolite particles prior to dispersion in the polymer matrix reduced the stress at the... 

Estimation of Polymer Sizes by Gel Permeation Chromatography. The copolymer (1 mg) was dissolved in 1 ml of phosphate buffered saline (PBS), pH 7.4, and applied to a column of Sephacryl S-300 (1 X 108 cm) or Sephacryl S-400 (1 x 114 cm). The column was eluted with PBS at a flow rate of 0.2 ml/min. The elution profile of the copolmer was monitored by its absorbance at 214 nm. Bovine serum albumin (BSA) was chromatographed for comparative purposes and polyacrylamide standards (Modchrom, Inc.) were used. 

The FALLS or MALLS detector measures r-related values a differential refractive index (DRI) detector is used to measure concentration, and the SEC supplies samples containing fractionated polymer solutions allowing both molecular weight and MWD to be determined. Further, polymer shape can be determined. This combination represents the most powerful one, based on ease of operation, variety of samples readily used, cost, means to determine polymer size, shape, and MWD available today. 

The kinetics of polycondensation reactions might be expected to be similar to those found in condensation reactions of small molecules (evidence suggests that rate coefficients are independent of polymer size). Polyesterification reactions between dibasic carboxylic acids and glycols can be catalysed by strong acids. In the absence of added catalyst, it has been suggested that the acidic monomer should act as a catalyst, whereupon the rate of reaction should be given by... 

The two approaches to the problem of predicting the extent of reaction at the onset of gelation differ appreciably in their predictions of pc for the same system of reactants. The Carothers equation predicts the extent of reaction at which the number-average degree of polymerization becomes infinite. This must obviously yield a value of pc that is too large because polymer molecules larger than Xn are present and will reach the gel point earlier than those of size Xn. The statistical treatment theoretically overcomes this error, since it predicts the extent of reaction at which the polymer size distribution curve first extends into the region of infinite size. 

The typical effect of initiator chain transfer [Baysal and Tobolsky, 1952] can be seen graphically in Fig. 3-6. The decrease of polymer size due to chain transfer to initiator is much less than indicated from the Ci values because it is the quantity Ci[I]/[M], which affects Xn (Eq. 3-109b). The initiator concentrations are quite low (10 4 I0 2 M) in polymerization, and the ratio [I]/[M] is typically in the range 10 3-10 s. 

Figure 4-5 shows the viscosity-average molecular weights in the emulsion polymerizations of styrene of Fig. 4-3. The results are in line with Eq. 4-7 in that the polymer size increases with the emulsifier concentration.

Fe = 2.0, the polymer size increased, with 80% being in the 50k-300k fraction (Tab. 13.1). All these polymers invariably displayed a broad doublet which could be fitted to two closely overlapping Fe " doublets with quadrupole splittings at RT of... 

Figure 11-4 Typical distribution of polymer sizes determined on molecule and weight bases.

Figure 11-S Average polymer size and size distribution.

We can further describe the conversion and average polymer size using end-group analysis. We can write... 

In any polymerization process one must be concerned with removal of the coproduct (typically H2O or HCl) so that equilibrium limitations do not limit the polymer size. The removal of the product in condensation polymerization to attain higher polymer lengths is a major consideration in polymerization reactor design. This can be done by withdrawing water vapor or by using two phases so that the water and polymer migrate to different phases. 

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